Newtonian Creep Research Articles

Diffusion Creep and Grain Growth in Forsterite +20 vol% Enstatite Aggregates: 1. High‐Resolution Experiments and Their Data Analyses

AbstractWe conducted uniaxial compression and grain growth experiments on fine‐grained (~1 μm) forsterite +20 vol% enstatite aggregates. Based on analyses of the sensitivity of the strain rate as a function of stress, we find power law creep at low stress, Newtonian creep at intermediate stress, and again power law creep at high stress, which correspond to interface‐controlled diffusion creep, grain boundary diffusion (Coble) creep, and a dislocation‐controlled process, respectively. The creep rate of these samples is well expressed by a combination of strain rates of these three mechanisms where interface‐controlled and Coble creep rates are combined as series‐sequential processes, while the rate of the dislocation process is added with them as a parallel‐concurrent process. Mechanical data collected continuously during the application of a constant load but while slowly changing temperature were decomposed into data for every 1 °C, which allowed consideration of >600 mechanical data points from 1054 to 1370 °C. The data were analyzed using Bayesian statistics implementing a Markov chain Monte Carlo method imposed on the above constitutive equation, resulting in the best fit flow law parameters for interface‐controlled and Coble creep. Samples were annealed for 500 hr at various temperatures. A comparison of the final grain sizes as a function of temperature on an Arrhenius plot resulted in an activation energy for grain growth similar to that observed for grain boundary diffusion during Coble creep of these materials.

Tidal synchronization of an anelastic multi-layered body: Titan’s synchronous rotation

Tidal torque drives the rotational and orbital evolution of planet–satellite and star–exoplanet systems. This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the rotational frequencies increase if the orbital eccentricity increases. This behavior is characteristic in the classical Darwinian theories and in the homogeneous case of the creep tide theory. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies $$n/2,n,3n/2,2n,\ldots $$ . When the friction increases, attractors with differential rotations are destroyed, surviving only commensurabilities in which core and shell have the same velocity of rotation. We apply the theory to Titan. The main results are: (i) the rotational constraint does not allow us to confirm or reject the existence of a subsurface ocean in Titan; and (ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini’s observation (Meriggiola et al. in Icarus 275:183–192, 2016), we limit the possible value of the shell relaxation factor, when a deep subsurface ocean is assumed, to $$\gamma _s\lesssim 10^{-9}\,\hbox {s}^{-1}$$ , which corresponds to a shell’s viscosity $$\eta _s\gtrsim 10^{18}\,\hbox {Pa}\,\hbox {s}$$ , depending on the ocean’s thickness and viscosity values. In the case in which a subsurface ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell’s viscosity is one order higher.

Experimental and computational simulation studies on creep deformation mechanisms of a novel nanostructured Cu and Cu-10%Sn Alloy

This work presents experimental and computational simulation studies on creep deformation mechanisms of a novel nanostructured Cu and Cu -10% Sn alloy that prepared by mechanical alloying (MA) copper with elemental Tin. Mechanical Newtonian creep model is employed for computational simulation of creep deformation mechanism under low stress-high temperature and to justify the experimental findings. The observed behaviors are discussed and compared with the predications of the Nabarro–Herring (N–H) theory of directional diffusion. A simple theory based on the climb controlled generation of dislocations from a fixed density of sources is developed to explain the observed behavior. TEM and SEM investigations are convenient and powerful techniques for characterization of phases and a novel nano-grain structured of the resulting materials. The reduction of grain size to the nanometer scale improves their mechanical properties.

Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach

This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly from the solution of a non-homogeneous ordinary differential equation. Lags appear in the solution but as quantities determined from the solution of the equation and are not arbitrary external quantities plugged in an elastic model. The resulting lags of the tide components are increasing functions of their frequencies (as in Darwin's theory), but not small quantities. The amplitudes of the tide components depend on the viscosity of the body and on their frequencies; they are not constants. The resulting stationary rotations (pseudo-synchronous) have an excess velocity roughly proportional to $6ne^2/(\chi^2+1/\chi^2)$ ($\chi$ is the mean-motion in units of one critical frequency - the relaxation factor - inversely proportional to the viscosity) instead of the exact $6ne^2$ of standard theories. The dissipation in the pseudo-synchronous solution is inversely proportional to $(\chi+1/\chi)$. In the inviscid limit it is roughly proportional to the frequency (as in standard theories), but that behavior is inverted when the viscosity is high and the tide frequency larger than the critical frequency. For free rotating bodies, the dissipation is given by the same law, but now $\chi$ is the frequency of the semi-diurnal tide in units of the critical frequency. This approach fails to reproduce the actual tidal lags on Earth. In this case, to reconcile theory and observations, we need to assume the existence of an elastic tide superposed to the creeping tide. The theory is applied to several Solar System and extrasolar bodies and currently available data are used to estimate the relaxation factor $\gamma$ (i.e. the critical frequency) of these bodies.

Depressurized Cavities within High-strain Shear Zones: their Role in the Segregation and Flow of SiO2-rich Melt in Feldspar-dominated Rocks

We observe void growth and coalescence into cavity-bearing shear bands during deformation of wet synthetic anorthite aggregates containing53 vol. % silica-enriched melt. Samples were deformed in the Newtonian creep regime to high strain during torsion experiments at 11008C and 400MPa confining pressure. Localized cavity-bearing shear bands show an S^C’-geometry: the bands (C’) are oriented at about 308 to the compression direction of the imposed simple shear and the internal foliation (S) of the bands is rotated towards the horizontal external shear plane. Cavity-bearing shear bands started to nucleate in the sample periphery above a shear strain threshold of 2. Quartz crystallized from the water-saturated SiO2-rich melt within large cavities inside these bands, which requires that the melt is decompressed by4200MPa during their formation. The dynamically evolving cavities are sites of locally reduced pressure that collect the melt distributed in the adjacent matrix.Therefore, cavitation damage under ductile conditions may result in the development of an efficient melt channelling system controlling SiO2-rich melt flow in the lower crust. Electron backscatter diffraction analysis shows that the quartz inside the cavity bands has a crystallographic preferred orientation (CPO). The development of the CPO is explained by the preferred dissolution of crystals oriented with the rhombohedra and trigonal dipyramids orthogonal to the compression direction and by preferential growth of crystals aligned with their500014axis in the extension direction of the externally applied simple shear deformation.

Kinetics and Nanostructure Dependence of High Temperature-Low Stress Creep of Al and Al-0.3%Fe

The novel nanostructure of Al and Al{Fe were prepared by ball milling alumina with elemental Fe. The kinetics and nanostructure dependence of high temperature low stress Newtonian creep of Al and Al{0.3%Fe have been investigated and compared with the predications of the Nabarro{Herring (N{H) theory of directional difiusion. A simple theory based on the climb controlled generation of dislocations from a flxed density of sources is developed to explain the observed behavior. The dislocation density increases and subgrains form during the creep. Also, the presence of precipitates of FeAl3 reduces the creep rate of Al by absolute faster of 100 at the same stress and temperature, in spite of the fact that the grain size in the Al{0.3%Fe alloy is smaller by a factor of about 100 nm. The reduction of grain size to the nanometer scale improves their mechanical properties. Electron difiraction methods combined with transmission electron microscopy (TEM) and scanning electron microscopy (SEM) studies are a convenient and powerful technique for the characterization of the phases and grain structure of the resulting materials.

The influence of dolomite on the plastic flow of calcite: Rheological, microstructural and chemical evolution during large strain torsion experiments

Aggregates composed of calcite and dolomite have been deformed and annealed at high temperature (700–800 °C) and high pressure (300 MPa) to investigate the mutual effects of deformation and chemical reaction, strain partitioning, fabric development and phase segregation in a polyphase rock. Samples deformed in torsion displayed an almost Newtonian creep with stress exponent of 1.7 ± 0.3. Specimens were deformed up to a maximum shear strain of γ = 10 and developed a clear texture documented by electron back-scatter diffraction measurements in both calcite and dolomite. Both the texture and the foliation created during the large strain experiments display a monoclinic symmetry closely reproducing that of naturally deformed carbonate marbles, with the preferred orientation of the c-axes inclined against the sense of shear. Detailed microstructural investigation shows that grains are internally strain-free and that grain boundaries are preferentially aligned in straight segments, implying that deformation occurred through a combination of grain boundary sliding and diffusion processes accommodated by dislocation activity. Chemical investigations performed on both statically annealed and torsion samples indicate that deformation may have an important influence on the phase equilibrium of a reacting system. Calcite grains deformed with excess of dolomite with respect to the equilibrium were able to incorporate higher amounts of Mg within the calcite lattice than the static samples, as documented by electron probe microanalysis. Moreover, the above analysis documented that reaction rate was faster in torsion than in static experiments at the same conditions of pressure and temperature.

Preferred orientation of anorthite deformed experimentally in Newtonian creep

Synthetic anorthite aggregates were deformed in a Paterson gas deformation apparatus at confining pressures up to 400 MPa in torsion and axial compression at temperatures between 950 °C and 1200 °C. Samples deformed in torsion under Newtonian creep display development of texture (or crystallographic preferred orientation) as documented with synchrotron X-ray diffraction measurements. Complex diffraction patterns were deconvoluted with the Rietveld method to obtain quantitative texture information. Torsion samples deformed up to shear strains of 4 and samples deformed in compression at higher stresses to total strains of 0.3 develop clear textures. Texture and shape preferred orientation (SPO) of torsion samples display a monoclinic pattern with an asymmetry inclined against the sense of shear, consistent with polycrystal plasticity simulations that assume the deformation is accomplished by dislocation glide. These results show that a material deforming in linear-viscous creep can develop a strong texture, in striking contrast to the paradigm that the presence of a texture precludes low-stress Newtonian behavior. Our observations show that the presence or absence of crystallographic preferred orientation is not sufficient to uniquely infer the dominant rheological/mechanical regime, as sometimes applied for interpretation of seismic anisotropy in the Earth.

An evaluation of the rate-controlling flow process in Newtonian creep of polycrystalline ice

Using experimental data and theoretical calculation for Newtonian creep in polycrystalline ice, it is demonstrated that unlike most other materials, in which the rate-controlling flow process is edge dislocation climb under saturated condition, the rate-controlling flow process of polycrystalline ice is dislocation glide along the basal plane under a constant dislocation density. The dislocation density during Newtonian creep of ice is determined by the initial state instead of the magnitude of the Peierls stress. The transition stress (threshold) from power-law creep to Newtonian creep is controlled by the dislocation density instead of the Peierls stress. The activation energy of the Newtonian creep is similar to that of the self-diffusion due to the requirements of the diffusion of protons during dislocation glide.

Thermal creep mechanisms in V–4Cr–4Ti pressurized tube specimens

Pressurized thermal creep tubes of V–4Cr–4Ti have been examined following testing in the range 650–800 °C for tests lasting ∼10 4 h to provide comparison with tests on similar tubes following irradiation. It is found in all cases that creep results from dislocation motion. But the mechanism changes with increasing temperature and lower stress from one controlled by the climb and interaction of individual dislocations, to one controlled by sub-grain boundary structure that is created by relaxation of the interacting dislocations to lower energy planar arrays. This change in mechanism corresponds to a change from power law creep to Newtonian creep such that the stress exponent drops from ∼4 to ∼1. Although it is possible to explain the Newtonian response as Nabarro–Herring or Coble creep, it appears more likely that behavior is due to Harper–Dorn creep, in which case the change in response occurs at the Peierls stress.

Harper–Dorn creep: Controversy, requirements, and origin

This paper reviews the current status of research on Harper–Dorn creep, Newtonian creep behavior that was first reported by Harper and Dorn in their studies on the creep of Al at very low stresses and temperature near the melting point, and that, unlike Nabarro–Herring creep, is apparently independent of grain size, d. An examination of the results reported for Al under the conditions of small strains (∼0.01) and those of recent experiments performed at strains (>0.1) reveals that Harper–Dorn creep does not always occur in large-grained Al at very low stresses; that Harper–Dorn creep is Newtonian in nature only at very small strains (<0.01), and that its occurrence in large-grained Al ( d > 400 μm) requires two conditions: the dislocation density in the annealed samples is low (10 3–10 4 cm −2) and the purity level of the material is high (99.999%). It is shown that the aforementioned requirements for Harper–Dorn creep can provide a possible explanation for the conflicting evidence regarding the occurrence of Harper–Dorn creep in Al when creep tested at very low stresses. In addition, preliminary results on Harper–Dorn creep in Pb that were obtained in long-term tests lend support to the second requirement related to the purity level of the material.

Investigation of Newtonian creep in polycrystalline ice

The mechanism for Newtonian creep in polycrystalline ice has been studied. It is shown that the creep can be explained by dislocation glide along the basal plane with a constant dislocation density. The experimentally determined creep-rates agree well with the values calculated using Cole's constitutive model based on dislocation glide.

Creep characterization of alumina particulate reinforced alumino-silicate glass

Compressive creep studies on alumino-silicate glass reinforced with alumina powders of 0.2 μm particle size as a function of volume fraction showed that there was a significant increase in the creep resistance by about an order of magnitude in the 20 vol.% composite. In order to study the effect of particle size on creep resistance, composites reinforced with 20 vol.% of 1.2 and 6.5 μm alumina particle size were also characterized. It was found that the composite with 1.2 μm particle sized reinforcement gave the highest creep resistance. All the composites exhibited Newtonian viscous creep and showed no strain hardening even at strains up to 10%.

High‐Temperature Rheology of Calcium Aluminosilicate (Anorthite) Glass‐Ceramics under Uniaxial and Triaxial Loading

The high‐temperature creep behavior of two fine‐grained (∼3 μm) anorthite‐rich glass‐ceramics was characterized at ambient pressure and under a confining pressure of ∼300 MPa. Experiments were done at differential stresses of 15–200 MPa and temperatures of 1200°–1320°C. Of the two materials, one had a tabular (lathlike) grain structure with finely dispersed second phase of mullite, mostly in the form of ∼3–5 μm grains comparable to that of the primary anorthite phase, whereas the other had an equiaxed grain morphology with fine (∼400 nm) mullite precipitates concentrated at the anorthite grain boundaries. The results of creep experiments at ambient pressure showed that the material with the tabular grain structure had strain rates at least an order of magnitude faster than the equiaxed material. Creep in the tabular‐grained material at ambient pressure was accompanied by a significant extent of intergranular cavitation: pore‐volume analysis before and after creep in this material suggested that &gt;75% of the bulk strain was due to growth of these voids. The equiaxed material, in contrast, showed a smooth transition from Newtonian (n= 1) creep at low stresses to non‐Newtonian behavior at high stresses (n &gt; 2). Under the high confining pressure, the microstructures of both materials underwent significant changes. Grain‐boundary mullite precipitates in the undeformed, equiaxed‐grain material were replaced by fine (∼100 nm), intragranular precipitates of silliminate and corundum because of a pressure‐induced chemical reaction. This was accompanied by a significant reduction in grain size in both materials. The substantial microstructural changes at high confining pressure resulted in substantially lower viscosities for both materials. The absence of mullite precipitates at the grain boundaries changed the behavior of the equiaxed material to non‐Newtonian (n= 2) at a pressure of ∼300 MPa, possibly because of a grain‐boundary sliding mechanism; the tabular‐grained material showed Newtonian diffusional creep under similar conditions.

An investigation of the deformation mechanism in grain size-sensitive Newtonian creep

Creep of polycrystalline materials at low stresses often shows a linear relationship between strain rate and stress, and an inverse dependence on grain size squared or cubed. Attribution of this behavior to diffusional creep or grain boundary sliding (GBS) has evoked much confusion and controversy in the literature. A model is proposed to unify these two creep mechanisms. The model predicts a change in dominant mechanism from diffusional creep to GBS accommodated mainly by diffusion or by GBS itself as the amount of matter moved by diffusion decreases. Corresponding to this change, the model also predicts a spectrum of creep rate with the absolute value being dependent upon the extent of diffusion accommodation. Although experimental data exhibit scattering, most of them are in very good agreement with the prediction of the GBS model. Therefore, it is suggested that the Newtonian creep behavior with grain size dependence be induced by GBS rather than by conventional diffusional creep as believed before.

The development of slabs in the upper mantle: Insights from numerical and laboratory experiments

We have performed numerical and laboratory experiments to model subduction of oceanic lithosphere in the upper mantle from its beginnings as a gravitational instability to the fully developed slab. A two‐dimensional finite element code is applied to model Newtonian creep in the numerical experiments. Scaled analog media are used in the laboratory, a sand mixture models the brittle crust, silicone putty simulates creep in the lower crust and mantle lithosphere, and glucose syrup is the asthenosphere analog. Both model approaches show similar results and reproduce first‐order observations of the subduction process in nature based on density and viscosity heterogeneities in a Stokes flow model. Subduction nucleates slowly and a pronounced slab forms only when the viscosity contrast between oceanic plate and mantle is below a threshold. We find that the subduction velocity and angle are time‐dependent and increase roughly exponentially over tens of millions of years before the slab reaches the 670‐km discontinuity. The style of subduction is controlled by the prescribed velocity of convergence, the density contrast between the plates, and the viscosity contrast between the oceanic plate and the mantle. These factors can be combined in the buoyancy number F which expresses the ratio between driving slab pull and resisting viscous dissipation in the oceanic plate. Variations in F control the stress in the plates, the speed and the dip of subduction, and the rate of trench retreat, reproducing the contrasting styles of subduction observed in nature. The subduction rate is strongly influenced by the work of bending the lithosphere as it subducts.

Creep and fatigue properties of high temperature silicides and their composites

A review of creep and fatigue behavior of high temperature silicides and their composites is presented along with new results pertaining to titanium silicides and functionally graded materials . The emphasis was placed on the molybdenum disilicides and their composites in comparison to other silicides and high temperature ceramics. It was shown that the grain size effects on creep are significant in these materials. The effects were present not only in the Newtonian creep but persists even in the power-law creep, with grain size exponents of the order of 4.2. Factors that influenced the grain size effects were examined. This anomalous behavior, which appeared to be exhibited by some stoichiometric intermetallics , could not be explained by the currently known theories of grain boundary creep. Effects of alloying and reinforcement on creep rates were also discussed. The creep rates in other high temperature silicides were compared. It was shown that molybdenum disilicide with silicon nitride has a potential for high temperature applications in terms of its creep and oxidation resistance , although its creep resistance appears to be much less than that of an advanced Si 3 N 4 , such as AS800. Published results on fatigue crack growth in MoSi 2 and its composites were analyzed using the recently developed Unified Approach for Fatigue.

A new interpretation of the mechanisms in Newtonian creep of uranium dioxides

Newtonian creep data on both stoichiometric and hyperstoichiometric urania materials are analyzed. It is shown that there may be two distinct regimes: one is grain size sensitive, and the other grain size insensitive. Both qualitative and quantitative evaluations of these two regimes suggest that deformation in the grain size sensitive regime may be controlled by lattice diffusion-accommodated grain boundary sliding whereas that in the grain size insensitive regime by a dislocation process operating in Harper-Dorn creep.

Incorporation of peierls stress into deformation mechanism maps

Crystalline materials deform plastically by a number of alternative, often competing, mechanisms. For engineering and geological applications, it is essential to know the conditions under which a specific mechanism is dominant over others. Deformation mechanism maps offer such information in a compact diagrammatic form. Existing deformation maps usually include mechanisms such as power law (P-L) dislocation creep and diffusional creep. Harper-Dorn (H-D) creep which is a Newtonian dislocation creep, and grain boundary sliding creep were scarcely considered because of unavailability of experimental data. For dislocation creep, in a manner similar to diffusional creep, the rate equation is also determined from experimental data. Consequently, existing mechanism maps were mainly constructed for specific materials under conditions. Recently, the knowledge of P-L creep and H-D creep has been greatly expanded, in particular, the transition from P-L creep to H-D creep. It is now possible to predict reasonably these two kinds of creep, and therefore to construct a generalized deformation mechanism map, independent of materials. The objective of this paper is to construct such generalized mechanism maps.

A note on creep in a single-crystal, Ni- Based superalloy

Creep in metals, ceramics, and silicates has been shown to change, as the applies stress, {sigma}, decrease, from power law dislocation creep with a stress exponent, n, of 3 to 5 to Newtonian viscous flow with n = 1. Superalloys are the materials of choice for high-temperature, structural applications. Ni-base superalloys, in particular, are strengthened by coherent precipitates ({gamma}{prime}Ni3Al). Although power law creep has been observed in many cases, Newtonian creep had not yet been reported for these alloys. The objective of the present communication is to demonstrate Newtonian creep in the single crystal of a superalloy.